The great schism from eastern and western religion happened over a long period of time but finally came to a split in 1054. Over time the customs and they way of doing the religious practices in the east and the west changed. In the west their was strict celibacy whereas in the east you could become a priest even if you were married. These small changes alone were not enough to divide the east and the west but this along with all the other things just made the east side more foreign and odd to the westerners. Constantinople was the capitol of the eastern part of the roman empire that remained unconquered by the barbarians and over time the city of Rome diminished in its power and prestige whereas Constantinople grew more and more powerful. The people in the east wanted Constantinople to replace Rome as the center of the Catholic faith saying that Rome was now just a backwater place compared to the powerful city of Constantinople. They thought that Constantinople was the new Rome and should be more important or at least equal to the city of Rome. All of this and the pope excommunicating a popular priest and misunderstandings lead to the division of religion in the east and the west. Today we still see the Greek Orthodox church from the time of the great schism.
In the 9th and 10th centurys in France the power became very de-centralized due to the constant invasions from Vikings and Muslims the local lords took over protesting that towns people. The kings power decreased until in the late 10th century the Carolingian dynasty died out and Hugh Capet became king only having control over Paris and some of the out skirting towns. But over the course of the Capetian dynasty the kings regained more control of their lands. In 1190 Phillip the second Augustus became king. He took back the French lands that had been ruled over by the king of England. Fiefs( small pieces of land that a lord would give to a vassal for his service) owned by Vassals who had no heir were taken by the king, as well as fiefs controlled by Vassals who ignored their feudal obligations. Under Phillip the second power in France became much more centralized and more like what we think the French monarchy was today.